Why finiteness problem of CFL is decidable?

We know that every $$CFL$$ has infinite configuration space. Due to this equality problem is undecidable. But why finiteness property is decidable inspite having infinite configuration space?

The language generated by a grammar with no useless symbols/productions is finite if and only if there is no non-terminal $$A$$ so that $$A \Rightarrow^* \alpha A \beta$$. This is easy to check.
• $\Rightarrow^*$ means arrow $\Rightarrow$? Oct 12, 2021 at 22:49